Problem: Simplify the following expression: $ p = \dfrac{x - 9}{6x + 8} + \dfrac{8}{3} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{x - 9}{6x + 8} \times \dfrac{3}{3} = \dfrac{3x - 27}{18x + 24} $ Multiply the second expression by $\dfrac{6x + 8}{6x + 8}$ $ \dfrac{8}{3} \times \dfrac{6x + 8}{6x + 8} = \dfrac{48x + 64}{18x + 24} $ Therefore $ p = \dfrac{3x - 27}{18x + 24} + \dfrac{48x + 64}{18x + 24} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{3x - 27 + 48x + 64}{18x + 24} $ $p = \dfrac{51x + 37}{18x + 24}$